A First-Principles Study on the Multiferroic Property of Two-Dimensional BaTiO₃ (001) Ultrathin Film with Surface Ba Vacancy.

In this work, the multiferroic property of Ba-deficient BaTiO₃ (001) ultrathin film is studied employing the first-principles approach. The BaTiO₃ (001) ultrathin film is more energetically stable and behaves as a semiconductor relative to the (111) and (101) configurations, confirmed from the surface grand potential and electronic density of states. The electronic structures show that the O vacancy can switch the (001) film from a semi-conductor into a metal, while the Ba defect has a slight influence on the band gap, at a concentration of ~2.13%. In Ba-deficient (001) film, the spontaneous polarization pattern is changed and a spontaneous polarization parallel to the surface is observed. Furthermore, a magnetic moment is induced, and it is found to be originated from the O atoms in the supercell. Our results suggest that a strong magnetoelectric coupling occurs because the magnetic moment exhibits a 43.66% drop when the spontaneous polarization increases from 12.84 C/cm² to 23.99 C/cm² in the deficient BaTiO₃ with = 2 under the bi-axial compress stress field.